Manufacturers test their products before shipping them to their customers to screen out as many defective parts as practical so the shipped products will satisfy the demand of the customers.
As an example, the manufacturers of semiconductor devices produce product that are used in automobiles, aircrafts, smart phones, medical diagnostic tools and treatment equipment, and entertainment products such as televisions sets and video games, etc. The customer who incorporates a semiconductor device in its product expects the device to perform properly to the specification.
In turn, the semiconductor manufacturer depends on its vendors and suppliers for clean rooms, starting wafers, consumable chemicals including gases and metals, photo masks and reticles, design software tools, design terminals and computing equipment, manufacturing equipment including implanters, diffusion tools, CVD tools, etching equipment, testers, handlers, bake ovens, probe cards, wire-bonders, molding equipment, etc. And the semiconductor manufacturer expects that those deliverables be thoroughly tested accordingly.
Product testing is challenging. At the start of a product design phase, the design may have weaknesses that may take a few iterations to amend. The weaknesses may manifest themselves at test of initial production runs or pilot runs. Many parts may fail multiple tests and the total product yield is low. The challenge in testing during this phase is to correlate the fails to design flaws and fabrication process margins.
Once a new design has been adequately “debugged” and the process of fabrication has been “fine tuned,” one can expect the defective portion of the new production to decrease. The challenge of testing then is to separate the defects due to design and manufacturing shortcomings from defects due to a second cause—the random defects that may be beyond a manufacturer's control. Examples of this type of defects in the semiconductor manufacturing include those caused by the minutest impurities or crystal imperfections in the starting wafer, dust particles that escape the most stringent filtering system in the clean room, and the slightest perturbation in electric power supply system throughout the fabrication flow, etc.
Because the manufacturer strives for but can not expect every device it produces to perform as designed, testing remains necessary to screen out the portion of the products that for one reason or another fails to meet all the product specifications, particularly due to defects of random causes.
Statistics play an important role in modern testing, especially when products mature. At this stage, one expects the defective parts to become an increasingly small portion of the total production and therefore depends more heavily on statistical analysis techniques to sort out the failure mechanisms and to improve production yield.
One tool that is widely used in the art of manufacturing is the capability index. It is used to quantify the robustness of a design and the manufacturing process with which the designed product is fabricated. The capability index, or capability ratio, is a statistical measurement of product performance, that is, the probabilistic expectation of the percentage of a production to function within specification limits.
Most product performance specifications have an upper and a lower specification limits USL and LSL, and a target mean T, the tested mean is p and the variability, expressed as a standard deviation, is σ. The commonly-accepted capability indices expressed in these terms include Cp and Cpk, defined as follows:Cp=(USL−LSL)/6σ  (1)
where Cp is a measurement of what the product performance is capable of if the mean were to be centered between the specification limits, assuming the measured output are approximately normally distributed; andCpk=min [(USL−μ)/3σ, (μ−LSL)/3σ]  (2)
where Cpk is a measurement of what the product performance is capable of, when the mean may not be centered between the specification limits.
With the terms defined as above, the capability of a particular product can be readily qualified and thus easily apprehended. For example, when the Cpk of a product performance reaches or stays above one, one can expect that out of a million devices manufactured, no more than 2,700 devices will likely be outside of the specification limits assuming the test results follow a normal distribution; and when the Cpk reaches 1.67, then the number of fallouts should be smaller than 1 ppm.
As a product matures, the testing result in terms of Cpk will raise to reflect the increasing of the product yield. Traditionally when it reaches a preset number, the manufacturer has a choice regarding its future product testing. It may choose continuingly testing all products in order to screen out the few parts that would fail the test, or skipping the test or only testing a small sample of the future products as a sentinel against process shift but let the few failed parts escape.